A Latent Space Graded Response Model for Likert-Scale Psychological Assessments

In this study, we introduce a novel modeling approach for ordinal response data, extending the one-parameter graded response model. The proposed model incorporates unobserved interactions between respondents and items, represented as distances in a two-dimensional Euclidean space, referred to as an interaction map. This latent space graded response model (LSGRM) addresses potential violations of the conditional independence assumption shared by traditional main-effect-only psychometric models and offers a visualization tool for exploring conditional dependence in ordinal item response data. Through simulation and empirical studies, we illustrate the utility of the proposed approach in analyzing Likert-scale psychological assessment data. Also, by comparing the results with those from other models of different data modalities, we examined the impact of dichotomization and treating ordinal responses as continuous on conditional dependence.